We present a novel mathematical, physical and logical framework for describing an input image of the dynamics of physical fields, in particular the optic field dynamics. Our framework is required to be invariant under a particular gauge group, i.e., a group or set of transformations consistent with the symmetries of that physical field dynamics enveloping renormalisation groups. It has to yield a most concise field description in terms of a complete and irreducible set of equivalences or invariants. Furthermore, it should be robust to noise, i.e.,unresolvable perturbations (morphisms) of the physical field dynamics present below a specific dynamic scale,possibly not covered by the gauge group, do not affect Lyapunov or structural stability measures expressed inequivalences above that dynamic scale. The related dynamic scale symmetry encompasses then a gauge invariant similarity operator with which similarly prepared ensembles of physical field dynamics are probed and searched for partial equivalences coming about at higher scales.